A study of gammap-->KSigma processes in an isobar model at tree level is reported. By comparing model calculations to the published SAPHIR data, we explore the possible role of different isospin I=1/2 (N*) and I=3/2(Delta*) resonances in the reaction dynamics. In our analysis, the inclusion of the "missing" D-13(1895) resonance does only slightly improve the global description of the Sigma photoproduction data. More convincing signals for the presence of such a "missing" resonance emerged in the analysis of the isospin related gammap-->K(+)Lambda reaction. Various implementations of the nonresonant part of the Sigma photoproduction amplitude are presented. The sensitivity of the computed observables and extracted resonance parameters to the uncertainties inherent to the treatment of the nonresonant (background) diagrams are discussed.